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Thermoelasticity of a regularly inhomogeneous curved layer with wavy surfaces. (English. Russian original) Zbl 0678.73011

J. Appl. Math. Mech. 51, No. 6, 770-776 (1987); translation from Prikl. Mat. Mekh. 51, No. 6, 1000-1008 (1987).
Summary: A curved inhomogeneous anisotropic layer of variable thickness is considered that has wavy surfaces. It is assumed that the elastic, thermophysical characteristics of the layer material and the shape of its upper and lower surfaces are periodic in structure with a single periodicity cell (PC). The period of the structure is here comparable in magnitude with the layer thickness, which is assumed to be much less than the other linear dimensions of the body and the radius of curvature of its middle surface.
On the basis of a general scheme for taking the average of processes in periodic media, a method is developed which enables a transition to be made from a spatial quasistatic thermoelasticity problem to a system of thermoelasticity equations for an average shell whose effective and thermophysical coefficients are determined from the solution of local problems in a PC. Results obtained for the static theory of elasticity by the authors [ibid. 51, No.1, 68-75 (1987; Zbl 0653.73007)] are used. The heat conduction problem is averaged to determine the temperature components occurring in the equation of motion.
The model constructed enables thermoelastic strains, stresses and the temperature distribution to be obtained in shells and plates of composite or porous materials with a different kind of reinforcement of the periodic structure (waffle, ribbed, corrugated) in reinforced and grid- like shells and plates. In the limiting case of “smooth” surfaces and a homogeneous material, the thermoelasticity equations are obtained for shallow anisotropic shells and the heat conduction equations of anisotropic shells assuming a linear temperature distribution law over the thickness.

MSC:

74F05 Thermal effects in solid mechanics
74E05 Inhomogeneity in solid mechanics
74E30 Composite and mixture properties
74A15 Thermodynamics in solid mechanics
80A20 Heat and mass transfer, heat flow (MSC2010)

Citations:

Zbl 0653.73007
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References:

[1] Bakhvalov, N. S.; Panasenko, G. P., Averaging Processes in Periodic Media (1984), Nauka: Nauka Moscow · Zbl 0607.73009
[2] Sanchez-Palencia, E., Inhomogeneous Media and Oscillation Theory (1984), Mir: Mir Moscow, /Russian Translation/ · Zbl 0542.73006
[3] Kalamkarov, A. L.; Kudryavtsev, B. A.; Parton, V. Z., The problem of a curved layer of composite material with wavy surfaces of periodic structure, PMM, 51, 1 (1987) · Zbl 0653.73007
[4] Podstrigach, Ya. S.; Lomakin, V. A.; Kolyano, Yu. M., Thermoelasticity of Bodies of Inhomogeneous Structure (1984), Nauka: Nauka Moscow · Zbl 0567.73014
[5] Pobedrya, B. E., Mechanics of Composite Materials (1984), Izd. Mosk. Gos. Univ · Zbl 0555.73069
[6] Sedov, L. I., (Mechanics of a Continuous Medium, 1 (1973), Nauka: Nauka Moscow)
[7] Podstrigach, Ya. S.; Shvets, R. N., Thermoelasticity of Thin Shells (1978), Naukova Dumka: Naukova Dumka Kiev
[8] Ambartsumyan, S. A., General Theory of Anisotropic Shells (1974), Nauka: Nauka Moscow · Zbl 0086.38505
[9] Novozhilov, V. V., Theory of Thin Shells (1962), Sudpromgiz: Sudpromgiz Leningrad · Zbl 0085.18803
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